Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5193 |
| Fitting | C2×C3×#135 ⋊ C2 |
| Sylow | C3 ⋊ C2×#509 |
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,7)(8,15)(9,18)(10,12)(11,14)(13,16)(17,20)(19,21);(1,2)(7,12)(11,19)(13,18)(15,20);(4,5)(7,11)(8,14)(9,16)(12,19)(13,20)(15,18)(17,21);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10712312, #10712314, #10712333, … |
| maximal normal subgroup of | #10712312, #10712314, #10712333, … |
| maximal quotient of | C2×#70652, C2×#72078, C2×#70649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16469);